We can use EFK stack for Kubernetes Logging and Monitoring. We need a Kubernetes cluster with following capabilities.

1. Ability to run privileged containers.
2. Helm and tiller enabled.
3. Statefulsets and dynamic volume provisioning capability: Elasticsearch is deployed as stateful set on Kubernetes. It’s best to use latest version of Kubernetes (v 1.10 as of this writing)

Please refer https://platform9.com/blog/kubernetes-logging-and-monitoring-the-elasticsearch-fluentd-and-kibana-efk-stack-part-2-elasticsearch-configuration/ for step by step guide.

You can run filebeat to collect logs from kubernetes. Follow the instruction of documentation on link:

After you download kubernetes.yaml change:

- name: ELASTICSEARCH_HOST
  value: [your elastic search domain]
- name: ELASTICSEARCH_PORT
  value: "9200"
- name: ELASTICSEARCH_USERNAME
  value: elastic
- name: ELASTICSEARCH_PASSWORD
  value: changeme

Pay attention! You need admin privileges for creating filebeat ServiceAccount

Have you tried fluentd? Logging agent that collects logs and able to ship logs to Elastic search.

UPDATE

I just found some examples in kops repo. You can check here